Problem: Simplify the following expression: $a = \dfrac{x^2 + 2x - 24}{x + 6} $
Solution: First factor the polynomial in the numerator. $ x^2 + 2x - 24 = (x + 6)(x - 4) $ So we can rewrite the expression as: $a = \dfrac{(x + 6)(x - 4)}{x + 6} $ We can divide the numerator and denominator by $(x + 6)$ on condition that $x \neq -6$ Therefore $a = x - 4; x \neq -6$